Simulation Optimization is providing solutions to important practical problems previously beyond reach. This paper explores how new approaches are significantly expanding the power of Simulation Optimization for managing risk. Recent advances in Simulation Optimization technology are leading to new opportunities to solve problems more effectively. Specifically, in applications involving risk and uncertainty, Simulation Optimization surpasses the capabilities of other optimization methods, not only in the quality of solutions, but also in their interpretability and practicality. In this paper, we demonstrate the advantages of using a Simulation Optimization approach to tackle risky decisions, by showcasing the methodology on two popular applications from the areas of finance and business process design.

Whenever uncertainty exists, there is risk. Uncertainty is present when there is a possibility that the outcome of a particular event will deviate from what is expected. In some cases, we can use past experience and other information to try to estimate the probability of occurrence of different events. This allows us to estimate a probability distribution for all possible events. *Risk* can be defined as the probability of occurrence of an event that would have a negative effect on a goal. On the other hand, the probability of occurrence of an event that would have a positive impact is considered an *opportunity* (see Ref. 1 for a detailed discussion of risks and opportunities). Therefore, the portion of the probability distribution that represents potentially harmful, or unwanted, outcomes is the focus of risk management.

Risk management is the process that involves identifying, selecting and implementing measures that can be applied to mitigate risk in a particular situation.^{1} The objective of risk management, in this context, is to find the set of actions (i.e., investments, policies, resource configurations, etc.) to reduce the level of risk to acceptable levels. What constitutes an acceptable level will depend on the situation, the decision makers’ attitude towards risk, and the marginal rewards expected from taking on additional risk. In order to help risk managers achieve this objective, many techniques have been developed, both qualitative and quantitative. Among quantitative techniques, optimization has a natural appeal because it is based on objective mathematical formulations that usually output an optimal solution (i.e. set of decisions) for mitigating risk. However, traditional optimization approaches are prone to serious limitations.

In Section 2 of this paper, we briefly describe two prominent optimization techniques that are frequently used in risk management applications for their ability to handle uncertainty in the data; we then discuss the advantages and disadvantages of these methods. In Section 3, we discuss how Simulation Optimization can overcome the limitations of traditional optimization techniques, and we detail some innovative methods that make this a very useful, practical and intuitive approach for risk management. Section 4 illustrates the advantages of Simulation Optimization on two practical examples. Finally, in Section 5 we summarize our results and conclusions.

** ****Traditional Scenario-based Optimization**

Very few situations in the real world are completely devoid of risk. In fact, a person would be hard-pressed to recall a single decision in their life that was completely risk-free. In the world of deterministic optimization, we often choose to “ignore” uncertainty in order to come up with a unique and objective solution to a problem. But in situations where uncertainty is at the core of the problem – as it is in risk management – a different strategy is required.

In the field of optimization, there are various approaches designed to cope with uncertainty.^{2,3} In this context, the exact values of the parameters (e.g. the data) of the optimization problem are not known with absolute certainty, but may vary to a larger or lesser extent depending on the nature of the factors they represent. In other words, there may be many possible “realizations” of the parameters, each of which is a possible *scenario*.

Traditional scenario-based approaches to optimization, such as *scenario optimization* and *robust optimization*, are effective in finding a solution that is feasible for all the scenarios considered, and minimizing the deviation of the overall solution from the optimal solution for each scenario. These approaches, however, only consider a very small subset of possible scenarios, and the size and complexity of models they can handle are very limited.

*Robust Optimization*

Robust optimization may be used when the parameters of the optimization problem are known only within a finite set of values. The robust optimization framework gets its name because it seeks to identify a robust decision – i.e. a solution that performs well across many possible scenarios.

In order to measure the robustness of a given solution, different criteria may be used. Kouvelis and Yu identify three criteria: (1) Absolute robustness; (2) Robust deviation; and (3) Relative robustness. We illustrate the meaning and relevance of these criteria, by describing their robust optimization approach.